Rings whose Right Modules are Direct Sums of Indecomposable Modules

DOI10.2307/2042637zbMath0441.16016OpenAlexW4243341100MaRDI QIDQ3882594

Birge Zimmermann Huisgen

Publication date: 1979

Full work available at URL: https://doi.org/10.2307/2042637

zbMATH Keywords

cancellation propertyalgebraically compact modulesrings of finite representation typelocal endomorphism ringsdirect sums of indecomposable modulesdirect sum of finitely generated modulessolvable system of equations

Mathematics Subject Classification ID

Injective modules, self-injective associative rings (16D50) Free, projective, and flat modules and ideals in associative algebras (16D40) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Other classes of modules and ideals in associative algebras (16D80) Representation theory of associative rings and algebras (16Gxx)

Related Items (26)

A test for finite representation type ⋮ Unnamed Item ⋮ Modules with chain conditions for finite matrix subgroups ⋮ Indecomposable decompositions of finitely presented pure-injective modules ⋮ On left Köthe rings and a generalization of a Köthe-Cohen-Kaplansky theorem ⋮ Local rings whose modules are almost serial ⋮ Chase's lemma and its context ⋮ Zerlegungen von Moduln und Injektive über Ringoiden ⋮ Characterisations of ${\varSigma }$-pure-injectivity in triangulated categories and applications to endocoperfect objects ⋮ On K-absolutely pure complexes ⋮ (Sigma-) algebraic compactness of rings ⋮ Prime uniserial modules and rings ⋮ Superstability, Noetherian rings and pure-semisimple rings ⋮ On ﬡ_α‐complete filters ⋮ Unnamed Item ⋮ On the relation between K-flatness and K-projectivity ⋮ Noetherian rings whose modules are prime serial ⋮ Indecomposable decompositions of pure-injective objects and the pure-semisimplicity. ⋮ Rings of pure global dimension zero and Mittag-Leffler modules ⋮ On the Sparsity of Representations of Rings of Pure Global Dimension Zero ⋮ Strong Preinjective Partitions and Representation Type of Artinian Rings ⋮ Algebraic compactness of reduced powers over commutative perfect rings ⋮ Rings whose modules are direct sums of extending modules ⋮ $\Sigma $-pure injectivity and Brown representability ⋮ Rings of finite representation type and modules of finite Morley rank ⋮ SOME STABLE NON-ELEMENTARY CLASSES OF MODULES

Cites Work

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• Algebraically compact rings and modules
• Direct-sum representations of injective modules
• Purity and algebraic compactness for modules
• Rings whose modules have nice decompositions
• Modules with decompositions that complement direct summands
• On direct sums and products of modules
• Direct Products of Modules
• On Rings whose Left Modules are Direct Sums of Finitely Generated Modules
• Rein injektive direkte summen von moduln
• Note on Rings of Finite Representation Type and Decompositions of Modules
• A Krull-Schmidt Theorem for Infinite Sums of Modules

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